The cumulative distribution function (c.d.f.) of a discrete random variable $X$, written $F(x)$, is defined as $F(x) = P[X \le x]$, the probability that $X$ takes a value no larger than $x$. It is computed by adding up the p.m.f. values $p_i = P[X = x_i]$ over every possible value $x_i$ that is less than or equal to $x$, so $F$ is built directly from the p.m.f. by running totals. For a discrete random variable, $F(x)$ increases only in jumps at the possible values of $X$ and stays flat …